Extended depth of field optical systems

ABSTRACT

An imaging system is characterized at least by an ambiguity function (“AF”) and a point spread function (“PSF”). The AF is a function of parameters u and v related to a misfocus parameter ψ; the PSF is at least a function of ψ. The system includes (1) an image recording device, (2) an optical arrangement for imaging an object to the image recording device, and (3) a post processor that renders an in-focus electronic image over a range of distances between the object and the optical arrangement. The optical arrangement alters phase such that a main lobe of the AF is broader in v for a specific u. The PSF has a functionally different form for a specific ψ, in comparison to a PSF characterizing the system when the optical arrangement does not alter the phase for those specific values of u and ψ over the range of distances.

RELATED APPLICATIONS

This application is a continuation of commonly owned and copending U.S.patent application Ser. No. 09/070,969, filed on May 1, 1998, which is acontinuation-in-part of U.S. patent application Ser. No. 08/823,894filed on Mar. 17, 1997, now U.S. Pat. No. 5,748,371, which is acontinuation of application Ser. No. 08/384,257, filed Feb. 3, 1995, nowabandoned. U.S. Pat. No. 5,521,695, issued May 28, 1996 and entitled“Range Estimation Apparatus and Method,” is incorporated herein byreference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support awarded by the NationalScience Foundation and the Office of Naval Research. The Government hascertain rights in this invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to apparatus and methods for increasing the depthof field and decreasing the wavelength sensitivity of incoherent opticalsystems. This invention is particularly useful for increasing the usefulrange of passive ranging systems. The same techniques are applicable topassive acoustical and electromagnetic ranging systems.

2. Description of the Prior Art

Improving the depth of field of optical systems has long been a goal ofthose working with imaging systems. A need remains in the art for asimple imaging system, with one or only a few lenses, which none theless provides greatly expanded depth of field focusing. Depth of fieldrefers to the depth in the scene being imaged. Depth of focus refers tothe depth in the image recording system.

A drawback of simple optical systems is that the images formed with redlight focus in a different plane from the images formed with blue orgreen light. There is only a narrow band of wavelengths in focus at oneplane; the other wavelengths are out of focus. This is called chromaticaberration. Currently, extending the band of wavelengths that form anin-focus image is accomplished by using two or more lenses withdifferent indices of refraction to form what is called an achromaticlens. If it were possible to extend the depth of field of the system,the regions would extended where each wavelength forms an in-focusimage. If these regions can be made to overlap the system, after digitalprocessing, can produce (for example) a high resolution image at thethree different color bands of a television camera. The extended depthof focus system can, of course, be combined with an achromatic lens toprovide even better performance.

There are several other aberrations that result in misfocus.Astigmatism, for example, occurs when vertical lines and horizontallines focus at different planes. Spherical aberration occurs when radialzones of the lens focus at different planes. Field curvature occurs whenoff-axis field points focus on a curved surface. And temperaturedependent focus occurs when changes in ambient temperature affect thelens, shifting the best focus position. Each of these aberrations istraditionally compensated for by the use of additional lens elements.

The effects of these aberrations that causes a misfocus are reduced bythe extended depth of imaging system. A larger depth of field gives thelens designer greater flexibility in balancing the aberrations.

The use of optical masks to improve image quality is also a popularfield of exploration. For example, “Improvement in the OTF of aDefocussed Optical System Through the Use of Shaded Apertures”, by M.Mino and Y. Okano, Applied Optics, Vol. 10 No. 10, October 1971,discusses decreasing the amplitude transmittance gradually from thecenter of a pupil towards its rim to produce a slightly better image.“High Focal Depth By Apodization and Digital Restoration” by J.Ojeda-Castaneda et al, Applied Optics, Vol. 27 No. 12, June 1988,discusses the use of an iterative digital restoration algorithm toimprove the optical transfer function of a previously apodized opticalsystem. “Zone Plate for Arbitrarily High Focal Depth” by J.Ojeda-Castaneda et al, Applied Optics, Vol. 29 No. 7, March 1990,discusses use of a zone plate as an apodizer to increase focal depth.

All of these inventors, as well as all of the others in the field, areattempting to do the impossible: achieve the point spread function of astandard, in-focus optical system along with a large depth of field bypurely optical means. When digital processing has been employed, it hasbeen used to try to slightly clean up and sharpen an image after thefact.

SUMMARY OF THE INVENTION

The systems described herein give in-focus resolution over the entireregion of the extended depth of focus. Thus they are especially usefulfor compensating for misfocus aberrations such as astigmatism, fieldcurvature, chromatic aberration, and temperature-dependent focus shifts.

An object of the present invention is to increase depth of field in anincoherent optical imaging system by adding a special purpose opticalmask to the system that has been designed to make it possible fordigital processing to produce an image with in-focus resolution over alarge range of misfocus by digitally processing the resultingintermediate image. The mask causes the optical transfer function toremain essentially constant within some range away from the in-focusposition. The digital processing undoes the optical transfer functionmodifying effects of the mask, resulting in the high resolution of anin-focus image over an increased depth of field.

A general incoherent optical system includes a lens for focusing lightfrom an object into an intermediate image, and means for storing theimage, such as film, a video camera, or a Charge Coupled Device (CCD) orthe like. The depth of field of such an optical system is increased byinserting an optical mask between the object and the CCD. The maskmodifies the optical transfer function of the system such that theoptical transfer function is substantially insensitive to the distancebetween the object and the lens, over some range of distances. Depth offield post-processing is done on the stored image to restore the imageby reversing the optical transfer alteration accomplished by the mask.For example, the post-processing means implements a filter which is theinverse of the alteration of the optical transfer function accomplishedby the mask.

In general, the mask is located either at or near the aperture stop ofthe optical system or an image of the aperture stop. Generally, the maskis placed in a location of the optical system such that the resultingsystem can be approximated by a linear system. Placing the mask at theaperture stop or an image of the aperture stop may have this result.Preferably, the mask is a phase mask that alters the phase whilemaintaining the amplitude of the light. For example, the mask could be acubic phase modulation mask.

The mask may be utilized in a wide field of view single lens opticalsystem, or in combination with a self focusing fiber or lens, ratherthan a standard lens. A mask for extending the depth of field of anoptical system may be constructed by examining the ambiguity functionsof several candidate mask functions to determine which particular maskfunction has an optical transfer function which is closest to constantover a range of object distances and manufacturing a mask having themask function of that particular candidate. The function of the mask maybe divided among two masks situated at different locations in thesystem.

A second object of the invention is to increase the useful range ofpassive ranging systems. To accomplish this object, the mask modifiesthe optical transfer function to be object distance insensitive asabove, and also encodes distance information into the image by modifyingthe optical system such that the optical transfer function containszeroes as a function of object range. Ranging post-processing meansconnected to the depth of field post-processing means decodes thedistance information encoded into the image and from the distanceinformation computes the range to various points within the object. Forexample, the mask could be a combined cubic phase modulation and linearphase modulation mask.

A third object of this invention is to extend the band of wavelengths(colors) that form an in-focus image. By extending the depth of field ofthe system, the regions are extended where each wavelength forms anin-focus image. These regions can be made to overlap and the system,after digital processing, can produce a high resolution image at thethree different color bands.

A fourth object of this invention is to extend the depth of field ofimaging systems which include elements whose optical properties varywith temperature, or elements which are particularly prone to chromaticaberration.

A fifth object of this invention is to extend the depth of field ofimaging systems to minimize the effects of misfocus aberrations likespherical aberration, astigmatism, and field curvature. By extending thedepth of field the misfocus aberrations can have overlapping regions ofbest focus. After digital processing, can produce images that minimizethe effects of the misfocus aberrations.

A sixth object of this invention is to physically join the mask forextending depth of field with other optical elements, in order toincrease the depth of field of the imaging system without adding anotheroptical element.

Those having normal skill in the art will recognize the foregoing andother objects, features, advantages and applications of the presentinvention from the following more detailed description of the preferredembodiments as illustrated in the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a standard prior art imaging system.

FIG. 2 shows an Extended Depth of Field (EDF) imaging system inaccordance with the present invention.

FIG. 3 shows a mask profile for a Cubic-PM (C-PM) mask used in FIG. 2.

FIG. 4 shows the ambiguity function of the standard system of FIG. 1.

FIG. 5 shows a top view of the ambiguity function of FIG. 4.

FIG. 6 shows the OTF for the standard FIG. 1 system with no misfocus.

FIG. 7 shows the OTF for the standard FIG. 1 system with mild misfocus.

FIG. 8 shows the Optical Transfer Function for the standard FIG. 1system with large misfocus.

FIG. 9 shows the ambiguity function of the C-PM mask of FIG. 3.

FIG. 10 shows the OTF of the extended depth of field system of FIG. 2,with the C-PM mask of FIG. 3, with no misfocus and before digitalprocessing.

FIG. 11 shows the OTF of the C-PM system of FIG. 2 with no misfocus,after processing.

FIG. 12 shows the OTF of the C-PM system of FIG. 2 with mild misfocus(before processing).

FIG. 13 shows the OTF of the C-PM system of FIG. 2 with mild misfocus(after processing).

FIG. 14 shows the OTF of the C-PM system of FIG. 2 with large misfocus(before processing).

FIG. 15 shows the OTF of the C-PM system of FIG. 2 with large misfocus(after processing).

FIG. 16 shows a plot of the Full Width at Half Maximum (FWHM) of thepoint spread function (PSF) as misfocus increases, for the standardsystem of FIG. 1 and the C-PM EDF system of FIG. 2.

FIG. 17 shows the PSF of the standard imaging system of FIG. 1 with nomisfocus.

FIG. 18 shows the PSF of the standard system of FIG. 1 with mildmisfocus.

FIG. 19 shows the PSF of the standard system of FIG. 1 with largemisfocus.

FIG. 20 shows the PSF of the C-PM system of FIG. 2 with no misfocus,before digital processing.

FIG. 21 shows the PSF of the C-PM system of FIG. 2 with no misfocusafter processing.

FIG. 22 shows the PSF of the C-PM system of FIG. 2 with small misfocusafter processing.

FIG. 23 shows the PSF of the C-PM system of FIG. 2 with large misfocusafter processing.

FIG. 24 shows a spoke image from the standard system of FIG. 1 with nomisfocus.

FIG. 25 shows a spoke image from the standard system of FIG. 1, withmild misfocus.

FIG. 26 shows a spoke image from the standard FIG. 1 system, with largemisfocus.

FIG. 27 shows a spoke image from the FIG. 2 C-PM system with no misfocus(before processing).

FIG. 28 shows a spoke image from the FIG. 2 C-PM system with no misfocus(after processing).

FIG. 29 shows a spoke image from the FIG. 2 C-PM system with mildmisfocus (after processing).

FIG. 30 shows a spoke image from the FIG. 2 C-PM system with largemisfocus (after processing).

FIG. 31 shows an imaging system according to the present invention whichcombines extended depth of field capability with passive ranging.

FIG. 32 shows a phase mask for passive ranging.

FIG. 33 shows a phase mask for extended depth of field and passiveranging, for use in the device of FIG. 31.

FIG. 34 shows the point spread function of the FIG. 31 embodiment withno misfocus.

FIG. 35 shows the point spread function of the FIG. 31 embodiment withlarge positive misfocus.

FIG. 36 shows the point spread function of the FIG. 31 embodiment withlarge negative misfocus.

FIG. 37 shows the point spread function of the FIG. 31 embodiment withno extended depth of field capability and no misfocus.

FIG. 38 shows the optical transfer function of the FIG. 31 embodimentwith no extended depth of field capability and with large positivemisfocus.

FIG. 39 shows the optical transfer function of the FIG. 31 embodimentwith no extended depth of field capability and with large negativemisfocus.

FIG. 40 shows the optical transfer function of the extended depth offield passive ranging system of FIG. 31 with a small amount of misfocus.

FIG. 41 shows the optical transfer function of a passive ranging systemwithout extended depth of field capability and with a small amount ofmisfocus.

FIG. 42 shows an EDF imaging system similar to that of FIG. 2, withplastic optical elements used in place of the lens of FIG. 2.

FIG. 43 shows an EDF imaging system similar to that of FIG. 2, with aninfrared lens used in place of the lens of FIG. 2.

FIG. 44 shows a color filter joined with the EDF mask of FIG. 3.

FIG. 45 shows a combined lens/EDF mask according to the presentinvention.

FIG. 46 shows a combined diffractive grating/EDF mask according to thepresent invention.

FIG. 47 shows and EDF optical system similar to that of FIG. 2, the lenshaving misfocus aberrations.

FIG. 48 shows an EDF optical system utilizing two masks in differentlocations in the system which combine to perform the EDF function,according to the present invention.

FIG. 49 shows an EDF imaging system similar to that of FIG. 2, with aself focusing fiber used in place of the lens of FIG. 2.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 (prior art) shows a standard optical imaging system. Object 15 isimaged through lens 25 onto Charge Coupled Device (CCD) 30. Such asystem creates a sharp, in-focus image at CCD 30 only if object 15 islocated at or very close to the in-focus object plane. If the distancefrom the back principal plane of lens 25 to CCD 30 is d_(i), and focallength of lens 25 is f, the distance, d₀, from the front principal planeof lens 25 to object 15 must be chosen such that:

${\frac{1}{d_{o}} + \frac{1}{d_{i}} - \frac{1}{f}} = 0$in order for the image at CCD 30 to be in-focus. The depth of field ofan optical system is the distance the object can move away from thein-focus distance and still have the image be in focus. For a simplesystem like FIG. 1, the depth of field is very small.

FIG. 2 shows the interaction and operation of a multi-component extendeddepth of field system in accordance with the invention. Object 15 isimaged through optical mask 20 and lens 25 onto Charge Coupled Device(CCD) system 30, and image post-processing is performed by digitalprocessing system 35. Those skilled in the art will appreciate that anyimage recording and retrieval device could be used in place of CCDsystem 30.

Mask 20 is composed of an optical material, such as glass or plasticfilm, having variations in opaqueness, thickness, or index ofrefraction. Mask 20 preferably is a phase mask, affecting only the phaseof the light transmitted and not its amplitude. This results in a highefficiency optical system. However, mask 20 may also be an amplitudemask or a combination of the two. Mask 20 is designed to alter anincoherent optical system in such a way that the system response to apoint object, or the Point Spread Function (PSF), is relativelyinsensitive to the distance of the point from the lens 25, over apredetermined range of object distances. Thus, the Optical TransferFunction (OTF) is also relatively insensitive to object distance overthis range. The resulting PSF is not itself a point. But, so long as theOTF does not contain any zeroes, image post processing may be used tocorrect the PSF and OTF such that the resulting PSF is nearly identicalto the in-focus response of a standard optical system over the entirepredetermined range of object distances.

The object of mask 20 is to modify the optical system in such a way thatthe OTF of the FIG. 2 system is unaffected by the misfocus distance overa particular range of object distances. In addition, the OTF should notcontain zeroes, so that the effects of the mask (other than theincreased depth of field) can be removed in post-processing.

A useful method of describing the optical mask function P(x) (P(x) isdescribed in conjunction with FIGS. 3-30 below) is the ambiguityfunction method. It happens that the OTF equation for an optical systemcan be put in a form similar to the well known ambiguity functionA(u,v). The ambiguity function is used in radar applications and hasbeen extensively studied. The use and interpretation of the ambiguityfunction for radar systems are completely different from the OTF, butthe similarity in the form of the equations helps in working with theOTF. The ambiguity function is given by:A(u,v)=∫{circumflex over (P)}(x+u/2){circumflex over (P)}*(x−u/2)e^(j2πxv) dxwhere * denotes complex conjugate and where the mask function P(x) is innormalized coordinates:

${{\hat{P}(x)} = {\hat{P}\left( {x\;\frac{D}{2\pi}} \right)}},{{\hat{P}(x)} = {{0{x}} > \pi}}$with D being the length of the one-dimensional mask. The above assumestwo dimensional rectangularly separable masks for simplicity. Suchsystems theoretically can be completely described by a one dimensionalmask.

As is known to those skilled in the art, given a general optical maskfunction P(x), one can calculate the response of the incoherent OTF toany value of misfocus ψ by the equation:H(u,ψ)=∫({circumflex over (P)}(x+u/2)e ^(j(x+u/2)) ² ^(ψ))({circumflexover (P)}*(x−u/2)e ^(−j(x−u/2)) ² ^(ψ))dxThe independent spatial parameter x and spatial frequency parameter uare unitless because the equation has been normalized. ψ is a normalizedmisfocus parameter dependent on the size of lens 25 and the focus state:

$\psi = {\frac{L^{2}}{4\pi\;\lambda}\left( {\frac{1}{f} - \frac{1}{d_{0}} - \frac{1}{d_{i}}} \right)}$Where L is the length of the lens, λ is the wavelength of the light, fis the focal length of lens 25, d₀ is the distance from the frontprincipal plane to the object 15, and d_(i) is the distance from therear principal plane to the image plane, located at CCD 30. Given fixedoptical system parameters, misfocus ψ is monotonically related to objectdistance d₀.

It can be shown that the OTF and the ambiguity function are related as:H(u,ψ)=A(u,uψ/π)Therefore, the OTF is given by a radial slice through the ambiguityfunction A(u,v) that pertains to the optical mask function {circumflexover (P)}(x). This radial line has a slope of ψ/π. The process offinding the OTF from the ambiguity function is shown in FIGS. 4-8. Thepower and utility of the relationship between the OTF and the ambiguityfunction lie in the fact that a single two dimensional function, A(u,v),which depends uniquely on the optical mask function {circumflex over(P)}(x), can represent the OTF for all values of misfocus. Without thistool, it would be necessary to calculate a different OTF function foreach value of misfocus, making it difficult to determine whether the OTFis essentially constant over a range of object distances.

A general form of the one family of phase masks is Cubic phaseModulation (Cubic-PM). The general form is:P(x,y)=exp(j(αx ³ +βy ³ +γx ² y+δxy ²)), |x|≦π,|y|≦π

Choice of the constants, α, β, γ, and δ allow phase functions that arerectangularly separable (with γ=δ=0) to systems whose modulationtransfer functions (MTF's) are circularly symmetric (α=β=α₀, γ=δ=−3α₀).For simplicity we will use the symmetric rectangularly separable form,which is given by:P(x,y)=exp(jα(x ³ +y ³)),|x|≦π,|y|≦π

Since this form is rectangularly separable, for most analysis only itsone dimensional component must be considered:{circumflex over (P)}(x)=exp(jαx ³),|x|≦πwhere α is a parameter used to adjust the depth of field increase.

FIG. 3 shows the mask implementing this rectangularly separable cubicphase function. When α=0, the mask function is the standard rectangularfunction given by no mask or by a transparent mask. As the absolutevalue of α increases, the depth of field increases. The image contrastbefore post-processing also decreases as a increases. This is because asa increases, the ambiguity function broadens, so that it is lesssensitive to misfocus. But, since the total volume of the ambiguityfunction stays constant, the ambiguity function flattens out as itwidens.

For large enough α, the OTF of a system using a cubic PM mask can beapproximated by:

${{H\left( {u,\psi} \right)} \approx {\sqrt{\frac{\pi}{3{{\alpha\; u}}}}{\mathbb{e}}^{{- j}\;\frac{\alpha\; u^{3}}{4}}}},{u \neq 0}$H(u, ψ) ≈ 2, u = 0Appendix A gives the mathematics necessary to arrive at the above OTFfunction.

Thus, the cubic-PM mask is an example of a mask which modifies theoptical system to have a near-constant OTF over a range of objectdistances. The particular range for which the OTF does not vary much isdependent of α. The range (and thus the depth of field) increases withα. However, the amount that depth of field can be increased ispractically limited by the fact that contrast decreases as a increases,and eventually contrast will go below the system noise.

FIGS. 4 through 30 compare and contrast the performance of the standardimaging system of FIG. 1 and a preferred embodiment of the extendeddepth of field system of FIG. 2, which utilizes the C-PM mask of FIG. 3.

In the following description, the systems of FIG. 1 and FIG. 2 areexamined using three methods. First, the magnitude of the OTFs of thetwo systems are examined for various values of misfocus. The magnitudeof the OTF of a system does not completely describe the quality of thefinal image. Comparison of the ideal OTF (the standard system of FIG. 1when in focus) with the OTF under other circumstances gives aqualitative feel for how good the system is.

Second, the PSFs of the two systems are compared. The full width at halfmaximum amplitude of the PSFs gives a quantitative value for comparingthe two systems. Third, images of a spoke picture formed by the twosystems are compared. The spoke picture is easily recognizable andcontains a large range of spatial frequencies. This comparison is quiteaccurate, although it is qualitative.

FIG. 4 shows the ambiguity function of the standard optical system ofFIG. 1. Most of the power is concentrated along the v=0 axis, making thesystem very sensitive to misfocus. FIG. 5 is the top view of FIG. 4.Large values of the ambiguity function are represented by dark shades inthis Figure. The horizontal axis extends from −2π to 2π. As discussedabove, the projection of a radial line drawn through the ambiguityfunction with slope ψ/π determines the OTF for misfocus ψ. This radialline is projected onto the spatial frequency u axis. For example, thedotted line on FIG. 5 was drawn with a slope of 1/(2π). This linecorresponds to the OTF of the standard system of FIG. 1 for a misfocusvalue of ψ=½. The magnitude of this OTF is shown in FIG. 7.

FIG. 6 shows the magnitude of the OTF of the standard system of FIG. 1with no misfocus. This plot corresponds to the radial line drawnhorizontally along the horizontal u axis in FIG. 5.

FIG. 7 shows the magnitude of the OTF for a relatively mild misfocusvalue of ½. This OTF corresponds to the dotted line in FIG. 5. Even fora misfocus of ½, this OTF is dramatically different from the OTF of thein-focus system, shown in FIG. 6.

FIG. 8 shows the magnitude of the OTF for a rather large misfocus valueof =3. It bears very little resemblance to the in-focus OTF of FIG. 6.

FIG. 9 shows the ambiguity function of the extended depth of fieldsystem of FIG. 2 utilizing the C-PM mask of FIG. 3 (the C-PM system).This ambiguity function is relatively flat, so that changes in misfocusproduce little change in the system OTF. α, as previously defined, isset equal to three for this particular system, designated “the C-PMsystem” herein.

FIG. 10 shows the magnitude of the OTF of the C-PM system of FIG. 2before digital filtering is done. This OTF does not look much like theideal OTF of FIG. 6. However, the OTF of the entire C-PM EDF system(which includes filtering) shown in FIG. 11 is quite similar to FIG. 6.The high frequency ripples do not affect output image quality much, andcan be reduced in size by increasing α.

FIG. 12 shows the magnitude of the OTF of the C-PM system of FIG. 2 withmild misfocus (ψ=½), before filtering. Again, this OTF doesn't look likeFIG. 6. It does, however look like FIG. 10, the OTF for no misfocus.Thus, the same filter produces the final OTF shown in FIG. 13, whichdoes resemble FIG. 6.

FIG. 14 shows the magnitude of the OTF of THE C-PM system of FIG. 2 withlarge misfocus (ψ=3), before filtering. FIG. 15 shows the magnitude ofthe OTF of the entire C-PM system. Notice that it is the fact that theOTFs before processing in all three cases (no misfocus, mild misfocus,and large misfocus) are almost the same that allows the samepost-processing, or filter, to restore the OTF to near ideal.

Note that while the OTF of the FIG. 2 C-PM system is nearly constant forthe three values of misfocus, it does not resemble the ideal OTF of FIG.10. Thus, it is desirable that the effect of the FIG. 3 mask (other thanthe increased depth of field) be removed by post-processing before asharp image is obtained. The effect of the mask may be removed in avariety of ways. In the preferred embodiment, the function implementedby post-processor (preferably a digital signal processing algorithm in aspecial purpose electronic chip, but also possible with a digitalcomputer or an electronic or optical analog processor) is the inverse ofthe OTF (approximated as the function H(u), which is constant over ψ).Thus, the post-processor 35 must, in general, implement the function:

$\sqrt{\frac{3{{\alpha\; u}}}{\pi}{\mathbb{e}}^{j\;\frac{\alpha\; u^{3}}{4}}}$

FIGS. 16-23 show the Point Spread Functions (PSFs) for the standardsystem of FIG. 1 and the C-PM system of FIG. 2 for varying amounts ofmisfocus. FIG. 16 shows a plot of normalized Full Width at Half Maximumamplitude (FWHM) of the point spread functions versus misfocus for thetwo systems. The FWHM barely changes for the FIG. 2 C-PM system, butrises rapidly for the FIG. 1 standard system.

FIGS. 17, 18, and 19 show the PSFs associated with the FIG. 1 standardsystem for misfocus values of 0, 0.5, and 3, (no misfocus, mildmisfocus, and large misfocus) respectively. The PSF changes dramaticallyeven for mild misfocus, and is entirely unacceptable for large misfocus.

FIG. 20 shows the PSF for the FIG. 2 C-PM system with no misfocus,before filtering (post-processing). It does not look at all like theideal PSF of FIG. 17, but again, the PSF after filtering, shown in FIG.21 does. The PSFs of the FIG. 2 C-PM system for mild misfocus is shownin FIG. 22, and the PSF for the FIG. 2 C-PM system with large misfocusis shown in FIG. 23. All three PSFs from the entire system are nearlyindistinguishable from each other and from FIG. 17.

FIG. 24 shows an image of a spoke picture formed by the FIG. 1 standardsystem with no misfocus. FIG. 25 shows an image of the same pictureformed by the FIG. 1 standard system with mild misfocus. You can stilldiscern the spokes, but the high frequency central portion of thepicture is lost. FIG. 26 shows the FIG. 1 standard system image formedwith large misfocus. Almost no information is carried by the image.

FIG. 27 is the image of the spoke picture formed by the FIG. 2 C-PMsystem, before digital processing. The image formed after processing isshown in FIG. 28. The images formed by the complete FIG. 2 system withmild and large misfocus are shown in FIGS. 29 and 30, respectively.Again, they are almost indistinguishable from each other, and from theideal image of FIG. 24.

FIG. 31 shows an optical system according to the present invention forextended depth of field passive ranging. Passive ranging using anoptical mask is described in U.S. Pat. No. 5,521,695 entitled “RangeEstimation Apparatus and Method” by the present inventors, hereinincorporated by reference. U.S. Pat. No. 5,521,695 discusses systemscontaining range dependent null space, which is substantially similar tothe range dependent zeroes discussed below.

In FIG. 31, general lens system 40 has front principal plane (or focalplane) 42 and back principal plane 43. Generally, optical mask 60 isplaced at or near one of the principal planes, but mask 60 may also beplaced at the image of one of the principal planes, as shown in FIG. 31.This allows beam splitter 45 to generate a clear image 50 of the object(not shown). Lens 55 projects an image of back focal plane 43 onto mask60. Mask 60 is a combined extended depth of field and passive rangingmask. CCD 65 samples the image from mask 60. Digital filter 70 is afixed digital filter matched to the extended depth of field component ofmask 60. Filter 70 returns the PSF of the image to a point as describedabove. Range estimator 75 estimates the range to various points on theobject (not shown) by estimating the period of the range-dependant nullsor zeroes.

Briefly, passive ranging is accomplished by modifying the incoherentoptical system of FIG. 2 in such a way that range dependent zeroes arepresent in the Optical Transfer Function (OTF). Note that the OTF of theEDF system discussed above could not contain zeroes, because the zeroescannot be removed by post filtering to restore the image. In FIG. 31,however, zeroes are added to encode the wavefront with rangeinformation. To find the range associated with small specific blocks ofthe image, the period of zeroes within a block is related to the rangeto the object imaged within the block. U.S. Pat. No. 5,521,695 primarilydiscusses amplitude masks, but phase masks can also produce an OTF withzeroes as a function of object range, and without loss of opticalenergy. Current passive ranging systems can only operate over a verylimited object depth, beyond which it becomes impossible to locate thezeroes, because the OTF main lobe is narrowed, and the ranging zeroesget lost in the OTF lobe zeroes. Extending the depth of field of apassive ranging system makes such a system much more useful.

Consider a general mask 60 for passive ranging described mathematicallyas:

${{P(x)} = {\sum\limits_{S = 0}^{S - 1}{{\mu_{S}\left( {x - {sT}} \right)}{\mathbb{e}}^{j\;{w_{s}{({x - {sT}})}}}}}},{{x} \leq {\pi/S}}$${\mu_{s}(x)} = {{0\mspace{14mu}{for}\mspace{14mu}{x}} > \frac{\pi}{s}}$This mask is composed of S phase modulated elements μ_(s)(x) of lengthT, where S·T=2π. Phase modulation of each segment is given by theexponential terms. If the above mask is a phase mask then the segmentsμ_(s)(x), s=0, 1, . . . , s−1, satisfy |μ_(s)(x)|=1. A simple example ofthis type of mask is shown in FIG. 32. This is a two segment (S=2) phasemask where ω₀==π/2, ω₁=π/2.

FIG. 32 shows an example of a phase passive ranging mask 80, which canbe used as mask 60 of FIG. 31. This mask is called a Linear PhaseModulation (LPM) mask because each of the segments modulates phaselinearly. Mask 80 comprises two wedges or prisms 81 and 82 with reversedorientation. Without optional filter 85, the formed image is the sum ofthe left and right components. Optional filter 85 comprises two halves86 and 87, one under each wedge. Half 86 is orthogonal to half 87, inthe sense that light which passes through one half will not pass throughthe other. For example, the filters could be different colors (such asred and green, green and blue, or blue and red), or could be polarizedin perpendicular directions. The purpose of filter 85 is to allowsingle-lens stereograms to be produced. A stereogram is composed of twoimages that overlap, with the distance between the same point in eachimage being determined by the object range to that point.

FIG. 33 shows the optical mask function of a combined LPM passiveranging mask and Cubic-PM mask 60 of FIG. 31 which is suitable forpassive ranging over a large depth of field. This mask is described by:P(x)=μ(x)e ^(jαx) ³ e ^(jω) ⁰ ^(x)+μ(x−π)e ^(jα(x−π)) ³ e ^(jw) ¹^((x−π)),

-   -   where μ(x)=1 for 0≦x≦π,        -   0 otherwise            By using two segments for the LPM component of mask 60, two            lobes of the PSF will be produced.

The PSF of the imaging system of FIG. 31, using a mask 60 having theFIG. 33 characteristics, with misfocus ψ=0 (no misfocus), is shown inFIG. 34. This system will be called the EDF/PR system, for extendeddepth of field/passive ranging. The PSF has two peaks because of the twosegments of mask 60.

FIG. 35 shows the PSF of the EDF/PR system with ψ=10. The fact that ψ ispositive indicates that the object is on the far side of the in-focusplane from the lens. The two peaks of the PSF have moved closertogether. Thus, it can be seen that the misfocus (or distance fromin-focus plane) is related to the distance between the peaks of the PSF.The actual processing done by digital range estimator 75 is, of course,considerably more complicated, since an entire scene is received byestimator 75, and not just the image of a point source. This processingis described in detail in U.S. Pat. No. 5,521,695.

FIG. 36 shows the PSF of the EDF/PR system with ψ=−10. The fact that ψis negative indicates that the object is nearer to the lens than is thein-focus plane. The two peaks of the PSF have moved farther apart. Thisallows estimator 75 to determine not only how far the object is from thein focus plane, but which direction.

It is important to note that while the distance between the peaks of thePSF varies with distance, the peaks themselves remain narrow and sharpbecause of the EDF portion of mask 60 combined with the operation ofdigital filter 70.

FIG. 37 shows the PSF of a system with an LPM mask 80 of FIG. 31,without the EDF portion, and with no misfocus. Since there is nomisfocus, FIG. 37 is very similar to FIG. 34. FIG. 38 shows the PSF ofmask 80 without EDF and with large positive misfocus (ω=10). The peakshave moved together, as in FIG. 35. It would be very difficult, however,for any amount of digital processing to determine range from this PSFbecause the peaks are so broadened. FIG. 39 shows the PSF of mask 80with no EDF and large negative misfocus (ψ=−10). The peaks have movedapart, but it would be difficult to determine by how much because of thelarge amount of misfocus.

That is, FIG. 39 shows the PSF of the LPM system without extended depthof field capability and with large negative misfocus (ω=−10). The peakshave moved further apart, but again it would be very difficult todetermine the location of the peaks.

FIG. 40 shows the optical transfer function of the combined EDF and LPMsystem shown in FIG. 31, with a small amount of misfocus (ψ=1). Theenvelope of the OTF is essentially the triangle of the perfect system(shown in FIG. 6). The function added to the OTF by the ranging portionof the mask of FIG. 33 includes range dependent zeroes, or minima. Thedigital processing looks for these zeroes to determine the range todifferent points in the object.

FIG. 41 shows the optical transfer function of the FIG. 31 embodimentwith no extended depth of field capability and small misfocus (ψ=1). Theenvelope has moved from being the ideal triangle (shown in FIG. 6) tohaving a narrowed central lobe with side lobes. It is still possible todistinguish the range dependent zeroes, but it is becoming moredifficult, because of the low value of the envelope between the mainlobe and the side lobes. As the misfocus increases, the main lobenarrows and the envelope has low values over a larger area. Therange-dependant minima and zeroes tend to blend in with the envelopezeroes to the extent that digital processing 70, 75 cannot reliablydistinguish them.

FIG. 42 shows an optical system 100, similar to the imaging system ofFIG. 2, but utilizing plastic optical elements 106 and 108 in place oflens 25. Optical elements 106, 108 are affixed using spacers 102, 104,which are intended to retain elements 106, 108 at a fixed location inthe optical system, with a fixed spacing between elements 106, 108. Alloptical elements, and especially plastic elements, are subject tochanges in geometry as well as changes in index of refraction withvariations in temperature. For example, PMMA, a popular plastic foroptical elements, has an index of refraction that changes withtemperature 60 times faster than that of glass. In addition, spacers 102and 104 will change in dimension with temperature, growing slightlylonger as temperature increases. This causes elements 106, 108 to moveapart as temperature increases.

Thus, changes in temperature result in changes in the performance ofoptical systems like system 100. In particular, the image plane of anoptical system like system 100 will move with temperature. EDF mask 20,combined with digital processing 35, increases the depth of field of thesystem 100, reducing the impact of this temperature effect. In FIG. 42,mask 210 is located between elements 102 and 104, but mask 20 may alsobe located elsewhere in the optical system.

EDF mask 20 (combined with processing 35) also reduces the impact ofchromatic aberrations caused by elements 106, 108. Plastic opticalelements are especially prone to chromatic aberrations due to thelimited number of different plastics that have good optical properties.Common methods of reducing chromatic aberrations, such as combining twoelements having different indices of refraction, are usually notavailable. Thus, the increase of depth of field provided by the EDFelements 20, 35, is particularly important in systems including plasticelements.

FIG. 43 shows an infrared lens 112 used in place of lens 25 in theimaging system of FIG. 2. Dotted line 114 shows the dimensions of lens112 at an increased temperature. Infrared materials such as Germaniumare especially prone to thermal effects such as changes in dimension andchanges in index of refraction with changes in temperature. The changein index of refraction with temperature is 230 times that of glass. EDFfilter 20 and processing 35 increase the depth of field of opticalsystem 110, reducing the impact of these thermal effects.

Like plastic optical elements, infrared optical elements are more proneto chromatic aberration than glass elements. It is especially difficultto reduce chromatic aberration in infrared elements, due to the limitednumber of infrared materials available. Common methods of reducingchromatic aberrations, such as combining two elements having differentindices of refraction, are usually not available. Thus, the increase indepth of field provided by the EDF elements is particularly important ininfrared systems.

FIG. 44 shows a color filter 118 joined with EDF mask 20. In someoptical systems it is desirable to process or image only one wavelengthof light, e.g. red light. In other systems a grey filter may be used. Insystems utilizing a color filter, EDF mask 120 may be affixed to thecolor filter or formed integrally with the color filter of a singlematerial, to form a single element.

FIG. 45 shows a combined lens/EDF mask 124 (the EDF mask is not toscale). This element could replace lens 25 and mask 20 of the imagingsystem of FIG. 2, for example. In this particular example, the mask andthe lens are formed integrally. A first surface 126 implements thefocusing function, and a second surface 128 also implements the EDF maskfunction. Those skilled in the art will appreciate that these twofunctions could be accomplished with a variety of mask shapes.

FIG. 46 shows a combined diffractive grating/EDF mask 130. Grating 134could be added to EDF mask 132 via an embossing process, for example.Grating 134 may comprise a modulated grating, e.g. to compensate forchromatic aberration, or it might comprise a diffractive optical elementfunctioning as a lens or as an antialiasing filter.

FIG. 47 shows an EDF optical system similar to that of FIG. 2, whereinlens 142 exhibits misfocus aberrations. Misfocus aberrations includeastigmatism, which occurs when vertical and horizontal lines focus indifferent planes, spherical aberration, which occurs when radial zonesof the lens focus at different planes, and field curvature, which occurswhen off-axis field points focus on a curved surface. Mask 20, inconjunction with post processing 35 extend the depth of field of theoptical system, which reduces the effect of these misfocus aberrations.

FIG. 48 shows an optical system 150 utilizing two masks 152, 156 indifferent locations in the system, which combine to perform the EDF maskfunction of mask 20. This might be useful to implement verticalvariations in mask 152 and horizontal variations in mask 156, forexample. In the particular example of FIG. 48, masks 152, 156 arearrayed on either side of lens 154. This assembly could replace lens 25and mask 20 in the imaging system of FIG. 2, for example.

FIG. 49 shows an optical imaging system like that of FIG. 2, with lens25 replaced by a self focusing element 148. Element 148 focuses lightnot by changes in the thickness of the optical material across the crosssection of the element (such as the shape of a lens), but rather bychanges in the index of refraction of the material across the crosssection of the element.

While the exemplary preferred embodiments of the present invention aredescribed herein with particularity, those having normal skill in theart will recognize various changes, modifications, additions andapplications other than those specifically mentioned herein withoutdeparting from the spirit of this invention.

1. An imaging system characterized at least by an ambiguity function anda point spread function (PSF), which ambiguity function is a function ofa normalized spatial frequency parameter u and a vertical variable vrelated to a misfocus parameter ψ, and which PSF is at least a functionof the misfocus parameter ψ, the imaging system comprising: an imagerecording device for converting light imaged thereon into a storedimage; an optical arrangement for imaging light from an object to theimage recording device to generate the stored image, which light ischaracterized by at least phase; and a post processor for processing thestored image from the image recording device, in accordance with thePSF, to render an in-focus electronic image over a range of objectdistances between the object and the optical arrangement, wherein theoptical arrangement is configured for altering the phase such that amain lobe of the ambiguity function is broader in v for a given value ofu over an optical bandpass of the imaging system, and the PSF has afunctionally different form for a given value of ψ, in comparison to amain lobe of an ambiguity function, a PSF and the optical bandpass,respectively, characterizing the imaging system when the opticalarrangement does not alter the phase for those given values of u and ψover the range of object distances.
 2. An imaging system of claim 1, theimage recording device comprising a charge-coupled device (CCD).
 3. Animaging system of claim 1, wherein the optical arrangement is formed ofan optical material selected from glass and plastic.
 4. An imagingsystem of claim 3, the optical arrangement having variations in at leasta selected one of opaqueness, thickness, diffractive properties andindex of refraction to alter the phase of the light.
 5. An imagingsystem of claim 1, the optical arrangement implementing a cubic phasemodulation.
 6. An imaging system of claim 1,the post processorcomprising a digital signal processing algorithm.
 7. An imaging systemof claim 1, the post processor comprising an electronic chip.
 8. Animaging system of claim 1, the post processor implementing a function${\sqrt{\frac{3{{\alpha\; u}}}{\pi}}{\mathbb{e}}^{j\;\frac{\alpha\; u^{3}}{4}}},$where α is a parameter used to adjust the range of object distances andu is a normalized, unitless spatial frequency parameter, to remove animaging effect induced by the optical arrangement.
 9. An imaging systemof claim 1, the light further including amplitude, and wherein theoptical arrangement includes variations in at least a selected one ofopaqueness, thickness and index of refraction so as to affect both ofthe phase and the amplitude.
 10. An imaging system of claim 1, theoptical arrangement altering the phase at two different locations in theimaging system.
 11. A method for decreasing optical sensitivity tomisfocus-related aberrations in an optical system characterized at leastby an ambiguity function and a point spread function (PSF), whichambiguity function is a function of a normalized spatial frequencyparameter u and a vertical variable v related to a misfocus parameter ψ,and which PSF is at least a function of the misfocus parameter ψ, themethod comprising the steps of: imaging light from an object to form anoptical image, which light is characterized by at least phase; detectingthe optical image to generate a stored image; and post processing thestored image, in accordance with the PSF, to render an in-focuselectronic image over a range of object distances between the object andthe imaging system, wherein imaging includes altering at least phase ofthe light such that a main lobe of the ambiguity function is broader inv for a given value of u over an optical bandpass of the optical system,and the PSF has a functionally different form for a given value of ψ, incomparison to a main lobe of an ambiguity function, a PSF and theoptical bandpass, respectively, characterizing the optical systemwithout altering the phase for those given values of u and ψ, over therange of object distances.
 12. The method of claim 11, wherein alteringthe phase includes altering the phase at two different locations in theoptical system.
 13. A method for increasing a depth of field of anoptical system characterized at least by an ambiguity function and apoint spread function (PSF), which ambiguity function is a function of anormalized spatial frequency parameter u and a vertical variable vrelated to a misfocus parameter ψ, and which PSF is at least a functionof the misfocus parameter ψ, the method comprising: imaging light froman object to form an image, the light being characterized by phase andamplitude; forming a digital representation of the image; andelectronically processing the digital representation, wherein imagingincludes altering at least the phase while maintaining the amplitudesuch that a main lobe of the ambiguity function is broader in v for agiven value of u over an optical bandpass of the imaging system, and thePSF has a functionally different form in comparison to a main lobe of anambiguity function, a PSF and the optical bandpass, respectively,characterizing the optical system without altering the phase for thosegiven values of u and ψ, over a range of object distances between theobject and the optical system, and wherein electronically processingincludes modifying the digital representation in accordance with the PSFto render an in-focus electronic image over the range of objectdistances.
 14. The method of claim 13, wherein forming the digitalrepresentation of the image includes capturing the image with acharge-coupled device (CCD) array.
 15. The method of claim 13, whereinaltering at least the phase comprises modulating the phase with aselected one of a linear phase modulation and a cubic phase modulation.16. The method of claim 13, wherein altering at least the phasecomprises diffracting the light.
 17. The method of claim 13, furthercomprising storing the digital representation of the image for use inthe electronically processing.
 18. The method of claim 13, whereinelectronically processing comprises filtering the image.
 19. The methodof claim 13, wherein altering the phase includes altering the phase attwo different locations in the optical system.